最適化原理による地層面の推定

不等式データや傾斜データを用いた曲面の推定

抄録

We present the principle and the BASIC program of a new gridding method for the numerical determination of the optimal shape of a bedding plane using various types of geological field data, as a geological application of the non-linear optimization problem. The principle is similar to one in the previous paper (Shiono et al., 1986) .
We assume that no faults and overfolding exist i.e. the shape of a bedding plane is expressed by a single valued function z=f (x, y) . Geological data to be used consist of height-data and dip-data. Height-data include inequality type of data i.e. f (x_k, y_k) -z_k≤0 or f (x_k, y_k) -z_k≥0 locally and f (x, y) ≤V_max or f (x, y) ≥V_min regionally, as well as equality type i.e. f (x_k, y_k) -z_k=0. Dip-data are considered to give first derivatives of f (x, y) . We consider that these data give constraints of the function f (x, y), and select the smoothest function as the optimal bedding plane among functions which satisfy given data, using a functional J (f) : J (f) =m₁∫_R [f_x²+f_y²] dxdy+m₂∫_R [f_xx²+2f_xy²+f_yy²] dxdy as a measure of smoothness of a function f (x, y) .
Based on the principle, we present a BASIC program to (1) input obeserved data from file, (2) calculate the optimal bedding plane as a grid data, and (3) output the grid data into file.